Time-resolved polarization measurements of pulsars offer a unique insight into the geometry of their emission regions. Such measurements provide observational constraints on the different models proposed for the pulsar emission mechanisms. Optical polarization data of the Crab nebula were obtained from the Hubble Space Telescope (HST) archive. The data set consists of a series of observations of the nebula taken with the HST/Advanced Camera for Surveys (ACS). We produced polarization vector maps of the inner nebula and measured, for the first time, the degree of linear polarization (P.D.) and the position angle (P.A.) of the pulsar's integrated pulse beam, and of its nearby synchrotron knot. This yielded P.D. = 5.2 ± 0.3 per cent and P.A. = 105 1 ± 1 6 for the pulsar, and P.D. = 59.0 ± 1.9 per cent and P.A. = 124 7 ± 1 0 for the synchrotron knot. This is the first high-spatial resolution multi-epoch study of the polarization of the inner nebula and pulsar. None of the main features in the nebula shows evidence of significant polarization evolution in the period covered by these observations. The results for the pulsar are consistent with those obtained by S owikowska et al. using the high-time resolution photo-polarimeter - Optical Pulsar Timing Analyzer (OPTIMA), once the constant component (DC) component has been subtracted. Our results clearly prove that the knot is the main source of the DC component.